Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2873,2,Mod(1,2873)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2873, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2873.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2873 = 13^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2873.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(22.9410205007\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
Embeddings
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
comment: embeddings in the coefficient field
gp: mfembed(f)
Label | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 | −2.67537 | 2.45751 | 5.15759 | 0.281106 | −6.57474 | −1.86504 | −8.44773 | 3.03935 | −0.752062 | ||||||||||||||||||
1.2 | −2.64254 | 1.46805 | 4.98302 | −0.0678132 | −3.87939 | −1.50308 | −7.88276 | −0.844817 | 0.179199 | ||||||||||||||||||
1.3 | −2.49472 | −3.11411 | 4.22362 | 0.618182 | 7.76882 | −4.72094 | −5.54732 | 6.69767 | −1.54219 | ||||||||||||||||||
1.4 | −2.41725 | −0.507735 | 3.84308 | 3.07956 | 1.22732 | 2.78507 | −4.45519 | −2.74221 | −7.44406 | ||||||||||||||||||
1.5 | −2.02053 | 0.582439 | 2.08253 | −4.34572 | −1.17683 | −2.56687 | −0.166750 | −2.66076 | 8.78065 | ||||||||||||||||||
1.6 | −1.82901 | −2.04300 | 1.34526 | 0.271875 | 3.73665 | 4.28757 | 1.19752 | 1.17384 | −0.497260 | ||||||||||||||||||
1.7 | −1.43489 | 2.33667 | 0.0589148 | −3.18692 | −3.35288 | 0.527416 | 2.78525 | 2.46005 | 4.57289 | ||||||||||||||||||
1.8 | −1.40628 | −2.89533 | −0.0223681 | −1.22522 | 4.07165 | 0.00936402 | 2.84402 | 5.38294 | 1.72300 | ||||||||||||||||||
1.9 | −1.31344 | 0.425303 | −0.274872 | 3.50529 | −0.558610 | 0.533081 | 2.98791 | −2.81912 | −4.60400 | ||||||||||||||||||
1.10 | −1.29273 | 3.21172 | −0.328841 | −1.87655 | −4.15190 | −0.932954 | 3.01057 | 7.31515 | 2.42588 | ||||||||||||||||||
1.11 | −0.753456 | 2.73570 | −1.43230 | 2.41010 | −2.06123 | −5.26341 | 2.58609 | 4.48407 | −1.81590 | ||||||||||||||||||
1.12 | −0.746998 | −1.42111 | −1.44199 | −3.76269 | 1.06157 | −3.12469 | 2.57116 | −0.980436 | 2.81072 | ||||||||||||||||||
1.13 | −0.0660340 | −0.327789 | −1.99564 | −0.468371 | 0.0216452 | −1.39129 | 0.263848 | −2.89255 | 0.0309284 | ||||||||||||||||||
1.14 | 0.215338 | −1.43588 | −1.95363 | −3.78845 | −0.309200 | −4.72811 | −0.851366 | −0.938239 | −0.815797 | ||||||||||||||||||
1.15 | 0.546083 | 1.17298 | −1.70179 | −3.07632 | 0.640541 | 2.98745 | −2.02149 | −1.62413 | −1.67993 | ||||||||||||||||||
1.16 | 0.567809 | −3.15503 | −1.67759 | 4.05966 | −1.79145 | −3.59152 | −2.08817 | 6.95418 | 2.30511 | ||||||||||||||||||
1.17 | 0.971429 | 1.27585 | −1.05632 | 2.95868 | 1.23940 | −2.11860 | −2.96900 | −1.37221 | 2.87415 | ||||||||||||||||||
1.18 | 1.15956 | 2.62321 | −0.655417 | −2.43355 | 3.04178 | 1.00673 | −3.07912 | 3.88125 | −2.82185 | ||||||||||||||||||
1.19 | 1.36752 | −2.08674 | −0.129896 | −0.220301 | −2.85365 | 2.93976 | −2.91267 | 1.35449 | −0.301266 | ||||||||||||||||||
1.20 | 1.81467 | −2.15950 | 1.29304 | 2.71933 | −3.91879 | −3.75697 | −1.28290 | 1.66345 | 4.93470 | ||||||||||||||||||
See all 24 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(13\) | \(-1\) |
\(17\) | \(-1\) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 2873.2.a.y | ✓ | 24 |
13.b | even | 2 | 1 | 2873.2.a.z | yes | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2873.2.a.y | ✓ | 24 | 1.a | even | 1 | 1 | trivial |
2873.2.a.z | yes | 24 | 13.b | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2873))\):
\( T_{2}^{24} + 5 T_{2}^{23} - 24 T_{2}^{22} - 153 T_{2}^{21} + 187 T_{2}^{20} + 1957 T_{2}^{19} + \cdots - 113 \) |
\( T_{3}^{24} - T_{3}^{23} - 50 T_{3}^{22} + 52 T_{3}^{21} + 1075 T_{3}^{20} - 1161 T_{3}^{19} + \cdots - 17927 \) |
\( T_{5}^{24} + 11 T_{5}^{23} - 17 T_{5}^{22} - 591 T_{5}^{21} - 1092 T_{5}^{20} + 11892 T_{5}^{19} + \cdots - 853 \) |